3.96.52 \(\int (512 x-640 x^3+400 x^4-90 x^5+7 x^6+e^{10+2 e^{40}} (2 x+3 x^2)+e^{5+e^{40}} (64 x+48 x^2-56 x^3+10 x^4)) \, dx\)

Optimal. Leaf size=23 \[ \left (e^{5+e^{40}}+(-4+x)^2\right )^2 \left (x^2+x^3\right ) \]

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Rubi [B]  time = 0.03, antiderivative size = 98, normalized size of antiderivative = 4.26, number of steps used = 3, number of rules used = 0, integrand size = 70, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \begin {gather*} x^7-15 x^6+2 e^{5+e^{40}} x^5+80 x^5-14 e^{5+e^{40}} x^4-160 x^4+e^{2 \left (5+e^{40}\right )} x^3+16 e^{5+e^{40}} x^3+e^{2 \left (5+e^{40}\right )} x^2+32 e^{5+e^{40}} x^2+256 x^2 \end {gather*}

Antiderivative was successfully verified.

[In]

Int[512*x - 640*x^3 + 400*x^4 - 90*x^5 + 7*x^6 + E^(10 + 2*E^40)*(2*x + 3*x^2) + E^(5 + E^40)*(64*x + 48*x^2 -
56*x^3 + 10*x^4),x]

[Out]

256*x^2 + 32*E^(5 + E^40)*x^2 + E^(2*(5 + E^40))*x^2 + 16*E^(5 + E^40)*x^3 + E^(2*(5 + E^40))*x^3 - 160*x^4 -
14*E^(5 + E^40)*x^4 + 80*x^5 + 2*E^(5 + E^40)*x^5 - 15*x^6 + x^7

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=256 x^2-160 x^4+80 x^5-15 x^6+x^7+e^{5+e^{40}} \int \left (64 x+48 x^2-56 x^3+10 x^4\right ) \, dx+e^{2 \left (5+e^{40}\right )} \int \left (2 x+3 x^2\right ) \, dx\\ &=256 x^2+32 e^{5+e^{40}} x^2+e^{2 \left (5+e^{40}\right )} x^2+16 e^{5+e^{40}} x^3+e^{2 \left (5+e^{40}\right )} x^3-160 x^4-14 e^{5+e^{40}} x^4+80 x^5+2 e^{5+e^{40}} x^5-15 x^6+x^7\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.04, size = 22, normalized size = 0.96 \begin {gather*} \left (e^{5+e^{40}}+(-4+x)^2\right )^2 x^2 (1+x) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[512*x - 640*x^3 + 400*x^4 - 90*x^5 + 7*x^6 + E^(10 + 2*E^40)*(2*x + 3*x^2) + E^(5 + E^40)*(64*x + 48
*x^2 - 56*x^3 + 10*x^4),x]

[Out]

(E^(5 + E^40) + (-4 + x)^2)^2*x^2*(1 + x)

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fricas [B]  time = 0.56, size = 65, normalized size = 2.83 \begin {gather*} x^{7} - 15 \, x^{6} + 80 \, x^{5} - 160 \, x^{4} + 256 \, x^{2} + {\left (x^{3} + x^{2}\right )} e^{\left (2 \, e^{40} + 10\right )} + 2 \, {\left (x^{5} - 7 \, x^{4} + 8 \, x^{3} + 16 \, x^{2}\right )} e^{\left (e^{40} + 5\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((3*x^2+2*x)*exp(exp(20)^2+5)^2+(10*x^4-56*x^3+48*x^2+64*x)*exp(exp(20)^2+5)+7*x^6-90*x^5+400*x^4-640
*x^3+512*x,x, algorithm="fricas")

[Out]

x^7 - 15*x^6 + 80*x^5 - 160*x^4 + 256*x^2 + (x^3 + x^2)*e^(2*e^40 + 10) + 2*(x^5 - 7*x^4 + 8*x^3 + 16*x^2)*e^(
e^40 + 5)

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giac [B]  time = 0.12, size = 65, normalized size = 2.83 \begin {gather*} x^{7} - 15 \, x^{6} + 80 \, x^{5} - 160 \, x^{4} + 256 \, x^{2} + {\left (x^{3} + x^{2}\right )} e^{\left (2 \, e^{40} + 10\right )} + 2 \, {\left (x^{5} - 7 \, x^{4} + 8 \, x^{3} + 16 \, x^{2}\right )} e^{\left (e^{40} + 5\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((3*x^2+2*x)*exp(exp(20)^2+5)^2+(10*x^4-56*x^3+48*x^2+64*x)*exp(exp(20)^2+5)+7*x^6-90*x^5+400*x^4-640
*x^3+512*x,x, algorithm="giac")

[Out]

x^7 - 15*x^6 + 80*x^5 - 160*x^4 + 256*x^2 + (x^3 + x^2)*e^(2*e^40 + 10) + 2*(x^5 - 7*x^4 + 8*x^3 + 16*x^2)*e^(
e^40 + 5)

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maple [B]  time = 0.05, size = 71, normalized size = 3.09

method	result	size
default	\({\mathrm e}^{2 \,{\mathrm e}^{40}+10} \left (x^{3}+x^{2}\right )+{\mathrm e}^{{\mathrm e}^{40}+5} \left (2 x^{5}-14 x^{4}+16 x^{3}+32 x^{2}\right )+x^{7}-15 x^{6}+80 x^{5}-160 x^{4}+256 x^{2}\)	\(71\)
risch	\(x^{3} {\mathrm e}^{2 \,{\mathrm e}^{40}+10}+x^{2} {\mathrm e}^{2 \,{\mathrm e}^{40}+10}+2 x^{5} {\mathrm e}^{{\mathrm e}^{40}+5}-14 x^{4} {\mathrm e}^{{\mathrm e}^{40}+5}+16 x^{3} {\mathrm e}^{{\mathrm e}^{40}+5}+32 x^{2} {\mathrm e}^{{\mathrm e}^{40}+5}+x^{7}-15 x^{6}+80 x^{5}-160 x^{4}+256 x^{2}\)	\(87\)
gosper	\(x^{2} \left (x^{5}+2 x^{3} {\mathrm e}^{{\mathrm e}^{40}+5}-15 x^{4}+{\mathrm e}^{2 \,{\mathrm e}^{40}+10} x -14 x^{2} {\mathrm e}^{{\mathrm e}^{40}+5}+80 x^{3}+{\mathrm e}^{2 \,{\mathrm e}^{40}+10}+16 \,{\mathrm e}^{{\mathrm e}^{40}+5} x -160 x^{2}+32 \,{\mathrm e}^{{\mathrm e}^{40}+5}+256\right )\)	\(88\)
norman	\(x^{7}+\left (-14 \,{\mathrm e}^{{\mathrm e}^{40}} {\mathrm e}^{5}-160\right ) x^{4}+\left (2 \,{\mathrm e}^{{\mathrm e}^{40}} {\mathrm e}^{5}+80\right ) x^{5}+\left ({\mathrm e}^{2 \,{\mathrm e}^{40}} {\mathrm e}^{10}+16 \,{\mathrm e}^{{\mathrm e}^{40}} {\mathrm e}^{5}\right ) x^{3}+\left ({\mathrm e}^{2 \,{\mathrm e}^{40}} {\mathrm e}^{10}+32 \,{\mathrm e}^{{\mathrm e}^{40}} {\mathrm e}^{5}+256\right ) x^{2}-15 x^{6}\)	\(93\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((3*x^2+2*x)*exp(exp(20)^2+5)^2+(10*x^4-56*x^3+48*x^2+64*x)*exp(exp(20)^2+5)+7*x^6-90*x^5+400*x^4-640*x^3+5
12*x,x,method=_RETURNVERBOSE)

[Out]

exp(exp(20)^2+5)^2*(x^3+x^2)+exp(exp(20)^2+5)*(2*x^5-14*x^4+16*x^3+32*x^2)+x^7-15*x^6+80*x^5-160*x^4+256*x^2

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maxima [B]  time = 0.35, size = 65, normalized size = 2.83 \begin {gather*} x^{7} - 15 \, x^{6} + 80 \, x^{5} - 160 \, x^{4} + 256 \, x^{2} + {\left (x^{3} + x^{2}\right )} e^{\left (2 \, e^{40} + 10\right )} + 2 \, {\left (x^{5} - 7 \, x^{4} + 8 \, x^{3} + 16 \, x^{2}\right )} e^{\left (e^{40} + 5\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((3*x^2+2*x)*exp(exp(20)^2+5)^2+(10*x^4-56*x^3+48*x^2+64*x)*exp(exp(20)^2+5)+7*x^6-90*x^5+400*x^4-640
*x^3+512*x,x, algorithm="maxima")

[Out]

x^7 - 15*x^6 + 80*x^5 - 160*x^4 + 256*x^2 + (x^3 + x^2)*e^(2*e^40 + 10) + 2*(x^5 - 7*x^4 + 8*x^3 + 16*x^2)*e^(
e^40 + 5)

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mupad [B]  time = 8.61, size = 75, normalized size = 3.26 \begin {gather*} x^7-15\,x^6+\left (2\,{\mathrm {e}}^{{\mathrm {e}}^{40}+5}+80\right )\,x^5+\left (-14\,{\mathrm {e}}^{{\mathrm {e}}^{40}+5}-160\right )\,x^4+\left (16\,{\mathrm {e}}^{{\mathrm {e}}^{40}+5}+{\mathrm {e}}^{2\,{\mathrm {e}}^{40}+10}\right )\,x^3+\left (32\,{\mathrm {e}}^{{\mathrm {e}}^{40}+5}+{\mathrm {e}}^{2\,{\mathrm {e}}^{40}+10}+256\right )\,x^2 \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(512*x + exp(2*exp(40) + 10)*(2*x + 3*x^2) + exp(exp(40) + 5)*(64*x + 48*x^2 - 56*x^3 + 10*x^4) - 640*x^3 +
400*x^4 - 90*x^5 + 7*x^6,x)

[Out]

x^5*(2*exp(exp(40) + 5) + 80) - x^4*(14*exp(exp(40) + 5) + 160) + x^3*(16*exp(exp(40) + 5) + exp(2*exp(40) + 1
0)) + x^2*(32*exp(exp(40) + 5) + exp(2*exp(40) + 10) + 256) - 15*x^6 + x^7

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sympy [B]  time = 0.07, size = 88, normalized size = 3.83 \begin {gather*} x^{7} - 15 x^{6} + x^{5} \left (80 + 2 e^{5} e^{e^{40}}\right ) + x^{4} \left (-160 - 14 e^{5} e^{e^{40}}\right ) + x^{3} \left (e^{10} e^{2 e^{40}} + 16 e^{5} e^{e^{40}}\right ) + x^{2} \left (256 + e^{10} e^{2 e^{40}} + 32 e^{5} e^{e^{40}}\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((3*x**2+2*x)*exp(exp(20)**2+5)**2+(10*x**4-56*x**3+48*x**2+64*x)*exp(exp(20)**2+5)+7*x**6-90*x**5+40
0*x**4-640*x**3+512*x,x)

[Out]

x**7 - 15*x**6 + x**5*(80 + 2*exp(5)*exp(exp(40))) + x**4*(-160 - 14*exp(5)*exp(exp(40))) + x**3*(exp(10)*exp(
2*exp(40)) + 16*exp(5)*exp(exp(40))) + x**2*(256 + exp(10)*exp(2*exp(40)) + 32*exp(5)*exp(exp(40)))

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